Persistence in Seasonally Forced Epidemiological Models and Seasonally Varying Predator-Prey Models Via the Basic Reproduction Number

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Hashemian, Zahra | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52428 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaraki, Mahmoud
Abstract:
In this study, we will examine persistence of various kinds of seasonally forced epidemiological models and seasonally varying predator-prey models. The results of our study regarding persistence of the models will be shown via basic reproduction number. We will show that, in the framework of our study and under some conditions, persistence is obtained as long as the basic reproduction number is bigger than one. We will also prove that, in the framework of our study and under sufficient conditions, if the basic reproduction number is smaller than one, the species under discussion won’t survive in the predator-prey models, and the disease(s) would go extinct in the epidemiological models.After stating the theorems, we will give corresponding examples. We will show that our results are flexible in many ways, and, thus, they are suitable and sufficient to prove persistence of a large class of epidemiological and ecological models, so that there would be no need to check every single model
Keywords:
Predator-Prey Model ; Epidemic Models ; Basic Reproduction Number ; Persistence ; Seasonality

No TOC